Comparison of laboratory and numerically observed scalar fields of an internal wave attractor

Abstract

Observations of internal gravity wave beams are frequently accompanied by theory that is purely two-dimensional, or two-dimensional numerical models. Although qualitative agreement between such models and laboratory experiments has been demonstrated, quantitative comparison has only been possible in a limited range of cases. Here, we present a quantitative comparison for internal wave attractors in the laboratory and a two-dimensional non-hydrostatic numerical model. To make a closer connection with previous theoretical work, the experimental and numerical results are presented in terms of the streamfunction and density perturbation, rather than the measured velocity and density gradient fields. The streamfunction is commonly used in the two-dimensional descriptions, e.g. to predict spatial patterns found in an enclosed stratified fluid in the laboratory. We demonstrate that, although the laboratory experiment in a narrow tank is only semi-two-dimensional, the flow is well described by two-dimensional internal wave theory and the numerical model reproduces quantitatively comparable attractors. The observed streamfunction field is compared with theoretical predictions, addressing an open question on the form of the streamfunction for internal wave attractor in a trapezoidal domain. The streamfunction has a simple spatial structure with sharp gradients at the attractor separating regions of nearly constant value outside the attractor.